Math

Math functions and constants: Math.Sqrt(2.0), Math.Max(a, b), Math.PI, …

double area = Math.PI * r * r;
int clamped = Math.Clamp(value, 0, 255);

The trigonometric functions use radians (Math.DegreesToRadians converts). For integer trigonometry without floating point (e.g. on a 68000) there is FastTrig.

Constants

Name	Description
`PI`	The ratio of a circle’s circumference to its diameter, π (3.14159…).
`E`	The base of the natural logarithm, e (2.71828…).
`Tau`	The ratio of a circle’s circumference to its radius, τ = 2π (6.28318…).

PI

const double PI = 3.141592653589793

The ratio of a circle’s circumference to its diameter, π (3.14159…).

E

const double E = 2.718281828459045

The base of the natural logarithm, e (2.71828…).

Tau

const double Tau = 6.283185307179586

The ratio of a circle’s circumference to its radius, τ = 2π (6.28318…).

Functions

Name	Description
`Abs`	The absolute value of `x`.
`Min`	The smaller of `a` and `b`.
`Max`	The larger of `a` and `b`.
`Clamp`	`value` limited to the range from `min` to `max`.
`Sign`	The sign of `x`.
`Floor`	The largest integer that is not larger than `x` (rounds towards negative infinity): `Floor(-1.5)` is -2.
`Ceiling`	The smallest integer that is not smaller than `x` (rounds towards positive infinity): `Ceiling(1.2)` is 2.
`Truncate`	`x` without its fractional part (rounds towards zero): `Truncate(-1.7)` is -1.
`Round`	`x` rounded to the nearest integer; halves go to the even neighbour (2.5 becomes 2, 3.5 becomes 4), like C#.
`Sqrt`	The square root of `x`.
`Cbrt`	The cube root of `x` (also for a negative `x`).
`Pow`	`x` to the power of `y`.
`Exp`	e to the power of `x`.
`Log`	The natural logarithm (base e) of `x`.
`Log2`	The logarithm of `x` to base 2.
`Log10`	The logarithm of `x` to base 10.
`Hypot`	The length of the hypotenuse, `Sqrt(x * x + y * y)`, without overflowing in between.
`Sin`	The sine of the angle `x` (in radians).
`Cos`	The cosine of the angle `x` (in radians).
`Tan`	The tangent of the angle `x` (in radians).
`Asin`	The angle (in radians, -π/2 to π/2) whose sine is `x`.
`Acos`	The angle (in radians, 0 to π) whose cosine is `x`.
`Atan`	The angle (in radians, -π/2 to π/2) whose tangent is `x`.
`Atan2`	The angle (in radians, -π to π) of the point (`x`, `y`): unlike `Atan(y / x)` it knows the quadrant and handles `x == 0`.
`Sinh`	The hyperbolic sine of `x`.
`Cosh`	The hyperbolic cosine of `x`.
`Tanh`	The hyperbolic tangent of `x`.
`DegreesToRadians`	An angle in degrees converted to radians.
`RadiansToDegrees`	An angle in radians converted to degrees.
`Lerp`	Linear interpolation between `a` and `b`: `a + (b - a) * t`, so `a` for `t` = 0 and `b` for `t` = 1.
`IsNaN`	Whether `x` is NaN (“not a number”, e.g. the result of `0.0 / 0.0`).
`IsInfinity`	Whether `x` is positive or negative infinity.

Abs

int Abs(int x)

The absolute value of x.

int64 Abs(int64 x)

The absolute value of x.

float Abs(float x)

The absolute value of x.

double Abs(double x)

The absolute value of x.

Min

int Min(int a, int b)

The smaller of a and b.

int64 Min(int64 a, int64 b)

The smaller of a and b.

float Min(float a, float b)

The smaller of a and b.

double Min(double a, double b)

The smaller of a and b.

Max

int Max(int a, int b)

The larger of a and b.

int64 Max(int64 a, int64 b)

The larger of a and b.

float Max(float a, float b)

The larger of a and b.

double Max(double a, double b)

The larger of a and b.

Clamp

int Clamp(int value, int min, int max)

value limited to the range from min to max.

Returns min if value is smaller, max if it is larger, otherwise value.

int64 Clamp(int64 value, int64 min, int64 max)

value limited to the range from min to max.

Returns min if value is smaller, max if it is larger, otherwise value.

float Clamp(float value, float min, float max)

value limited to the range from min to max.

Returns min if value is smaller, max if it is larger, otherwise value.

double Clamp(double value, double min, double max)

value limited to the range from min to max.

Returns min if value is smaller, max if it is larger, otherwise value.

Sign

int Sign(int x)

The sign of x.

Returns -1 for a negative x, 0 for 0, 1 for a positive x.

int Sign(double x)

The sign of x.

Returns -1 for a negative x, 0 for 0 (and NaN), 1 for a positive x.

Floor

double Floor(double x)

The largest integer that is not larger than x (rounds towards negative infinity): Floor(-1.5) is -2.

Ceiling

double Ceiling(double x)

The smallest integer that is not smaller than x (rounds towards positive infinity): Ceiling(1.2) is 2.

Truncate

double Truncate(double x)

x without its fractional part (rounds towards zero): Truncate(-1.7) is -1.

Round

double Round(double x)

x rounded to the nearest integer; halves go to the even neighbour (2.5 becomes 2, 3.5 becomes 4), like C#.

Sqrt

double Sqrt(double x)

The square root of x.

Returns NaN for a negative x.

Cbrt

double Cbrt(double x)

The cube root of x (also for a negative x).

Pow

double Pow(double x, double y)

x to the power of y.

Exp

double Exp(double x)

e to the power of x.

Log

double Log(double x)

The natural logarithm (base e) of x.

Returns negative infinity for 0, NaN for a negative x.

Log2

double Log2(double x)

The logarithm of x to base 2.

Returns negative infinity for 0, NaN for a negative x.

Log10

double Log10(double x)

The logarithm of x to base 10.

Returns negative infinity for 0, NaN for a negative x.

Hypot

double Hypot(double x, double y)

The length of the hypotenuse, Sqrt(x * x + y * y), without overflowing in between.

Sin

double Sin(double x)

The sine of the angle x (in radians).

Cos

double Cos(double x)

The cosine of the angle x (in radians).

Tan

double Tan(double x)

The tangent of the angle x (in radians).

Asin

double Asin(double x)

The angle (in radians, -π/2 to π/2) whose sine is x.

Returns NaN if x is outside of -1 to 1.

Acos

double Acos(double x)

The angle (in radians, 0 to π) whose cosine is x.

Returns NaN if x is outside of -1 to 1.

Atan

double Atan(double x)

The angle (in radians, -π/2 to π/2) whose tangent is x.

Atan2

double Atan2(double y, double x)

The angle (in radians, -π to π) of the point (x, y): unlike Atan(y / x) it knows the quadrant and handles x == 0.

Sinh

double Sinh(double x)

The hyperbolic sine of x.

Cosh

double Cosh(double x)

The hyperbolic cosine of x.

Tanh

double Tanh(double x)

The hyperbolic tangent of x.

DegreesToRadians

double DegreesToRadians(double degrees)

An angle in degrees converted to radians.

RadiansToDegrees

double RadiansToDegrees(double radians)

An angle in radians converted to degrees.

Lerp

double Lerp(double a, double b, double t)

Linear interpolation between a and b: a + (b - a) * t, so a for t = 0 and b for t = 1.

IsNaN

bool IsNaN(double x)

Whether x is NaN (“not a number”, e.g. the result of 0.0 / 0.0).

IsInfinity

bool IsInfinity(double x)

Whether x is positive or negative infinity.